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Inegalitate in n variabile
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Inegalitate in n variabile
Posted:
Sun May 10, 2009 7:49 pm
by
alex2008
Fie
\( x_1,x_2,...,x_n> 0 \)
astfel incat
\( \sum_{k=1}^n\frac{1}{1+x_k}=1 \)
. Sa se demonstreze ca :
\( x_1x_2...x_n\ge n^{n+1} \)
Posted:
Sun May 10, 2009 9:16 pm
by
Marius Mainea
\( x_k=\frac{\sum_{i\neq k}a_i}{a_k} \)
si apoi AM-GM.